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Expresiones idénticas
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Expresiones con funciones
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sin((3/2)x)=1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\sin{\left(\frac{3 x}{2} \right)} = 1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$\frac{3 x}{2} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{3 x}{2} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
O
$$\frac{3 x}{2} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{3 x}{2} = 2 \pi n + \frac{\pi}{2}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{3}{2}$$
obtenemos la respuesta:
$$x_{1} = \frac{4 \pi n}{3} + \frac{\pi}{3}$$
$$x_{2} = \frac{4 \pi n}{3} + \frac{\pi}{3}$$
$$\sin{\left(\frac{3 x}{2} \right)} = 1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$\frac{3 x}{2} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{3 x}{2} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
O
$$\frac{3 x}{2} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{3 x}{2} = 2 \pi n + \frac{\pi}{2}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{3}{2}$$
obtenemos la respuesta:
$$x_{1} = \frac{4 \pi n}{3} + \frac{\pi}{3}$$
$$x_{2} = \frac{4 \pi n}{3} + \frac{\pi}{3}$$
Suma y producto de raíces
[src]
suma
pi -- 3
$$\frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
producto
pi -- 3
$$\frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
pi/3
Respuesta numérica
[src]
x1 = -7.33038267350814
x2 = 55.5014699534987
x3 = -91.1061872401435
x4 = 47.1238901451077
x5 = 89.0117915374304
x6 = 34.5575191545974
x7 = -65.973445764965
x8 = -86.9173964058804
x9 = -36.6519146164944
x10 = -78.5398160671119
x11 = 1.04719723035021
x12 = -70.1622358133488
x13 = 30.368728557747
x14 = 68.0678406232729
x15 = 97.3893719471524
x16 = 72.2566310277182
x17 = -15.7079632965688
x18 = 59.6902604466305
x19 = -82.7286062234857
x20 = 51.3126803210339
x21 = 59.6902606051614
x22 = 63.8790510980994
x23 = 21.9911485852019
x24 = 89.0117921945182
x25 = 34.5575190254396
x26 = 51.3126796779143
x27 = -40.8407041585847
x28 = -61.7846554920017
x29 = -49.2182851576903
x30 = -28.2743337109378
x31 = 93.2005817199255
x32 = 38.7463096532239
x33 = 76.4454211251683
x34 = 1.04719789505839
x35 = 97.3893725546444
x36 = 63.8790507168974
x37 = -19.8967524531002
x38 = -40.8407048312981
x39 = -32.4631238400231
x40 = 93.2005823894749
x41 = 30.3687289117458
x42 = 13.6135683840417
x43 = -86.9173970757308
x44 = 80.63421157648
x45 = -74.3510262081665
x46 = -95.2949769348727
x47 = -91.1061866280936
x48 = 9.4247776591012
x49 = 84.8230019493851
x50 = 21.9911486616243
x51 = 84.8230013819433
x52 = 76.4454206780174
x53 = 5.23598808347229
x54 = -99.4837675424695
x55 = 42.9350999336178
x56 = -49.2182846243209
x57 = -74.3510259306603
x58 = -82.7286068795523
x59 = -95.2949773829705
x60 = 5.23598741935005
x61 = 72.2566310778853
x62 = 55.5014704726783
x63 = -7.3303830689021
x64 = -57.5958654073412
x65 = 9.42477824412579
x66 = -36.6519139878069
x67 = 13.6135680276684
x68 = 80.6342112457163
x69 = -99.4837675092727
x70 = -53.4070752903267
x71 = -45.0294943619788
x72 = -70.1622351533757
x73 = 42.9350993021016
x74 = -3.14159292945294
x75 = -19.8967526317057
x76 = 101.578162278555
x77 = 17.802358505396
x78 = -24.0855436053597
x79 = -45.0294950069103
x80 = 47.1238894723151
x81 = -57.5958661314289
x82 = -28.2743337356367
x83 = -53.4070750552514
x84 = -78.5398166250153
x85 = -11.5191734090774
x86 = 38.7463091551107
x87 = -3.14159233776395
x88 = 26.1799388483782
x89 = 17.8023589160787
x90 = -11.5191731923443
x91 = -32.4631243184515
x91 = -32.4631243184515